Human beings solve complex problems through critical thinking, where reasoning and evaluation are intertwined to converge toward correct solutions. However, most existing large language models (LLMs) treat the reasoning and verification as separate processes: they either generate reasoning without explicit self-checking or rely on external verifiers to detect errors post hoc. The former lacks immediate feedback, while the latter increases system complexity and hinders synchronized learning. Motivated by human critical thinking, we propose Stepwise Think-Critique (STC), an end-to-end trainable framework in which a single LLM emits a structured, step-level critique inline with each reasoning step. STC is trained with reinforcement learning that complements reasoning rewards with a critique-consistency reward derived from final-answer correctness, jointly optimizing reasoning correctness and critique reliability. On five mathematical reasoning benchmarks, STC improves Pass@1 by 7.2% over the 1.5B base model and attains 67.4% step-level critique F1, surpassing seven external process reward models evaluated at their per-dataset oracle thresholds---a step toward LLMs with built-in critical thinking.
Jiaqi Xu, Cuiling Lan, Xuejin Chen et al.· 0 citations
Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions.
Haiteng Zhao, Junhao Shen, Yiming Zhang et al.· 0 citations
Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM) framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research. We have identified two critical challenges of mathematical research compared to competition, the intrinsic complexity of research problems and the requirement of procedural rigor. To address these challenges, AIM incorporates two core strategies: an exploration mechanism to foster longer solution paths, and the pessimistic reasonable verification method to ensure reliability. This early version of AIM already exhibits strong capability in tackling research-level tasks. We conducted extensive experiments across several real-world mathematical topics and obtained promising results. AIM is able to autonomously construct substantial portions of proofs and uncover non-trivial insights within each research area. These findings highlight the potential of LRMs in mathematical discovery and suggest that LRM-based agent systems could significantly accelerate mathematical research in the future.
Yuanhang Liu, Yanxing Huang, Yanqiao Wang et al.· 0 citations
AI copilots represent a new generation of AI-powered systems designed to assist users, particularly knowledge workers and developers, in complex, context-rich tasks. As these systems become more embedded in daily workflows, personalization has emerged as a critical factor for improving usability, effectiveness, and user satisfaction. Central to this personalization is preference optimization: the system's ability to detect, interpret, and align with individual user preferences. While prior work in intelligent assistants and optimization algorithms is extensive, their intersection within AI copilots remains underexplored. This survey addresses that gap by examining how user preferences are operationalized in AI copilots. We investigate how preference signals are sourced, modeled across different interaction stages, and refined through feedback loops. Building on a comprehensive literature review, we define the concept of an AI copilot and introduce a taxonomy of preference optimization techniques across pre-, mid-, and post-interaction phases. Each technique is evaluated in terms of advantages, limitations, and design implications. By consolidating fragmented efforts across AI personalization, human-AI interaction, and language model adaptation, this work offers both a unified conceptual foundation and a practical design perspective for building user-aligned, persona-aware AI copilots that support end-to-end adaptability and deployment.
Saleh Afzoon, Ali Shahsavandi, Phuong Thao Huynh et al.· 0 citations
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Large reasoning models (LRMs) have achieved remarkable success on complex tasks, yet their tendency to "overthink" leads to inefficiencies. Although "save-thinking" prompts are intended to mitigate this issue, we find that LRMs still frequently enter the "Still-thinking" mode instead of the expected "No-thinking" mode, especially on difficult queries. To analyze this behavioral divergence, we examine LRMs from three perspectives: confidence at the thinking-termination boundary, divergence in internal attention distributions, and attention allocation across prompt segments. We find that high perplexity is associated with later Still-thinking behavior, and that Still-thinking cases allocate more attention to the original question. Based on these observations, we propose an attention intervention method to regulate this behavior. While this intervention suppresses explicit thinking, it also causes a drop in accuracy, suggesting that the suppressed reasoning behavior is often useful for correctness. Our work provides confidence- and attention-level evidence for this behavior, highlighting the trade-off between instruction following, inference efficiency, and reasoning correctness.
Rongzhi Zhu, Yi Liu, Jiancheng Wang et al.· 0 citations
Autonomous robots powered by deep learning face a fundamental auditability challenge: when incidents occur, investigators cannot reconstruct why the system made specific decisions. This paper presents TRACE (Transparent Reasoning Architecture for Credible Execution), a decision framework that ensures every autonomous action can be traced back to sensor evidence through documented causal chains. The framework organizes decision-making into four auditable layers: Semantic Perception for evidence-grounded entity recognition, Belief Reasoning for probabilistic state estimation with causal graphs, Action Synthesis for constraint-aware planning with counterfactual documentation, and Execution Verification for compliance monitoring. TRACE is model-agnostic yet designed to integrate learning-based perception modules (CNNs, transformers) while preserving decision-level auditability. We evaluate the framework using three objective metrics: Evidence Traceability (sensor-to-decision linkage), Decision Reconstructability (post-hoc analysis capability), and Temporal Continuity (audit trail completeness). Experimental evaluation on warehouse robot navigation demonstrates that TRACE achieves 98.6% evidence traceability, 99.0% temporal continuity, and 98.1% decision reconstructability across 500 simulated decision cycles. Post-hoc methods like LIME provide feature attributions but lack the artifact structure needed for decision-level reconstruction. The framework addresses EU AI Act requirements for high-risk system transparency and contributes to Explainable AI for safety-critical autonomous systems.
Competitive programming has become a key test of large language model reasoning, with international competitions such as IOI and ICPC representing its most challenging settings. We present an end-to-end specialization pipeline combining large-scale problem curation, synthetic reasoning traces, supervised fine-tuning (SFT), and reinforcement learning (RL). Using 22,000 curated problems, we train Nemotron-3-Nano-CC (30B-A3B) with SFT and RL and Nemotron-3-Ultra-CC (550B-A55B) with SFT alone. We further introduce GenCorrect, a feedback-driven test-time compute strategy that iteratively generates, evaluates, and refines diverse solutions. On IOI 2025, Nano-CC improves from 130 points to 291 after post-training and to 468 with GenCorrect, exceeding the gold threshold of 438.3 while Ultra-CC reaches 502. Guided by these results, we develop a competition-specific Ultra-CC system and evaluate it prospectively during IOI 2026. Under the same time, internet-access, and submission constraints as human contestants, it scores 535.4 out of 600, exceeding both the gold threshold of 361.12 and the top human score of 498.27. To our knowledge, this is the first AI system to outscore the highest-scoring human contestant on an IOI problem set.
Aleksander Ficek, Sean Narenthiran, Mehrzad Samadi et al.· 0 citations
For more than 20 years, the Model-RB benchmark frb100-40 remained an open challenge; since 2014, its public record had stood at 99 of 100 variables. We give a directly checkable 100-vertex independent set for its 4,000-vertex graph. Together with a verified partition into 100 cliques of size 40, the witness proves that the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. The stochastic run that found the witness is kept separate from this proof. We evaluated its added pair and triple repair operators in a preregistered campaign comprising 8,668 valid runs. The primary comparison found no detectable acceleration over base ULSA (hazard ratio 0.967, 95% confidence interval 0.915-1.023; p=0.248), and the factorial ablation reached the same conclusion. On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs, compared with 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates. With no events, the planned cross-solver hazard ratios remain unidentified. NuMVC ended with cover size 3,902 in 40 runs and 3,903 in 16. Exhaustive enumeration showed that none of the 108 unique recorded conflict-two states had a strictly improving group-aware CSP neighbor within Hamming radius three. The certificate settles the instance. The experiments characterize the search barrier, and the preregistered comparisons show no heuristic advantage.
People increasingly use language models to support life decisions. Many such decisions involve a probabilistic forecast: How likely is a major life event, a natural disaster, or an economic outcome? Users of language models may implicitly trust that these forecasts fall out of a coherent world model. In this paper, we evaluate the coherence of language model probabilistic forecasts through a procedure that builds on a theorem due to de Finetti. We elicit forecasts from language models across events generated from stock returns data. We then use linear programs to compute the largest Dutch-book profit - the profit an arbitrageur could guarantee by betting against model-generated probabilities - which we use as a measure of incoherence. Our procedure does not require outcome labels, so we can evaluate coherence even in settings where outcomes are not observed or have not yet resolved. We find substantial evidence of incoherence in language model forecasts. Such incoherence increases when there are richer logical relationships between events, and irrelevant contextual details can increase incoherence by an order of magnitude. We conclude by discussing how alternative training strategies may improve probabilistic coherence.
Training data attribution (TDA) aims to identify training examples that shape model behavior, but its intervention value depends on both which examples are selected and how they are modified. Influence functions (IF) estimate behavioral changes under infinitesimal reweighting, yet IF-selected examples often show limited advantages over random selection under conventional weight-based interventions. This raises the question of whether influential examples lack intervention value or whether reweighting fails to realize their behavioral leverage.We introduce influence-guided response rewriting, which uses IF to identify intervention targets and replaces their responses with behavior-aligned or behavior-opposed supervision while keeping instructions fixed. Across four open-weight LLMs, we compare rewriting and reweighting on the same influence-selected examples using epistemic abstention as our primary testbed. Response rewriting produces stronger, more persistent, and bidirectional behavioral shifts, while reweighting the same examples yields weak and inconsistent effects. Further analyses show that influence-selected examples provide greater rewriting leverage than alternative selectors, with changes remaining concentrated on target-relevant behaviors. The same qualitative contrast extends to safety refusal. These results distinguish the local reweighting effects captured by influence estimates from the broader intervention leverage of the examples they identify, motivating intervention-aware evaluation of TDA methods.
Yuzhang Luo, Chenpeng Wang, Jianhui Chen et al.· 0 citations
Large language models now answer medical questions with expert-level performance. However, the context these systems act on can be misleading, and misleading context can corrupt a model's medical judgment. To understand how misleading context corrupts this judgment, we examine the model's susceptibility to the context, disclosure of it, mechanism of corrupted reasoning, and monitorability of the decision. On the medical reasoning subset of MedMisBench, a clinician-reviewed question-answering benchmark of 8,627 questions, we inject two types of misleading context cues, fabricated evidence and a bare assertion. We test three reasoning models, two that expose their full reasoning trace and one frontier model that exposes only its response. All three are more susceptible to the assertion than to the fabricated evidence, adopting the asserted answer 10 to 27 points more often. The misleading cues are disclosed in 81 to 98% of traces but only 7 to 90% of responses, and the assertion is disclosed less often than evidence based cues. Resampling from reasoning traces without disclosure shows the two cues corrupt reasoning differently, evidence entering early and accumulating while the assertion redirects the conclusion near its end. An LLM monitor catches 78% of corrupted decisions at 5% false positives when reading an open model's trace with guidance, against at most 32% from any response. The misleading context that models are most susceptible to is disclosed least, and was caught reliably only from an open reasoning trace, which frontier providers withhold.
Polymeric materials are central to modern technologies, with applications ranging from energy to health and transportation. Although AI has made significant advances in materials discovery, the hierarchical structure of polymers across multiple length scales makes them inherently difficult to represent in a unified and physically meaningful way. Here we introduce HiPoly, a polymer-native AI framework that processes complete polymer descriptions through a three-level hierarchical graph architecture built on the G2RINS representation. HiPoly encodes stochastic inter-monomer connectivity, composition, and molecular weight directly within its architecture, using physically motivated design principles that mirror the multi-scale nature of polymeric systems. The framework establishes an end-to-end AI-driven workflow from experimental formulation data to property prediction, generative molecular design, and physics-based validation through molecular simulations, all unified by a single polymer representation. We demonstrate state-of-the-art prediction accuracy for thermophysical properties of multi-component polymer systems, with ablation studies confirming that each hierarchical design choice contributes independently to model performance. As an example, the generative design pathway is applied here to the discovery of sustainable alternatives to persistent fluorinated polymers, where it is possible to identify and independently validate PFAS-free candidates with target surface-energy properties. This work demonstrates how polymer-native AI can accelerate discovery by linking representation, prediction, and design across complex polymer chemistries.
Ge Sun, Gervasio Zaldivar, Yuan Tian et al.· 0 citations
